Find the Inverse 3/x-10

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

The LCM of one and any expression is the expression.

Multiply each term in ${\displaystyle \frac{3}{y}=x+10}$ by ${\displaystyle y}$.

Simplify the left side.

Rewrite the equation as ${\displaystyle xy+10y=3}$.

Factor ${\displaystyle y}$ out of ${\displaystyle xy+10y}$.

Divide each term in ${\displaystyle y(x+10)=3}$ by ${\displaystyle x+10}$ and simplify.

Set up the composite result function.

Evaluate ${\displaystyle f^{-1}(\frac{3}{x}-10)}$ by substituting in the value of ${\displaystyle f}$ into ${\displaystyle f^{-1}}$.

Simplify the denominator.

Multiply the numerator by the reciprocal of the denominator.

Cancel the common factor of ${\displaystyle 3}$.

Set up the composite result function.

Evaluate ${\displaystyle f\left(\frac{3}{x+10}\right)}$ by substituting in the value of ${\displaystyle f^{-1}}$ into ${\displaystyle f}$.

Simplify each term.

Combine the opposite terms in ${\displaystyle x+10-10}$.